Application of DerivativeHard

Question

The function f(x) is

Options

A.increasing on (0, ∞)

B.decreasing on (0, ∞)

C.increasing on (0,π / e) , decreasing on (π / e, ∞)

D.decreasing on (0, π / e) increasing on (π / e, ∞)

Given, f(x)

f′(x)

.....(i)
when x > 0,π + x > e + x
∴ log(π + x) > log(e + x)
and

On multiplying above equations, we get

......(i)
From Eqs. (i) and (ii),
f′(x) < 0
∴ f(x) is decreasing for x ∈ (0, ∞)

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